Analytical modeling for transient probe response in eddy current testing
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Analytical models that describe the electromagnetic field interactions arising between field generating and sensing coils in close proximity to conducting structures can be used to enhance analysis and information extracted from signals obtained using electromagnetic non-destructive evaluation technologies. A novel strategy, which enables the derivation of exact solutions describing all electromagnetic interactions arising in inductively coupled circuits due to a voltage excitation, is developed in this work. Differential circuit equations are formulated in terms of an arbitrary voltage excitation and of the magnetic fields arising in inductive systems, using Faraday’s law and convolution, and solved using the Fourier transform. The approach is valid for systems containing any number of driving and receiving coils, and include nearby conducting and ferromagnetic structures. In particular, the solutions account for feedback between a ferromagnetic conducting test piece and the driving and sensing coils, providing correct voltage response of the coils. Also arising from the theory are analytical expressions for complex inductances in a circuit, which account for real (inductive) and imaginary (loss) elements associated with conducting and ferromagnetic structures. A novel model-based method for simultaneous characterization of material parameters, which includes magnetic permeability, electrical conductivity, wall thickness and liftoff, is subsequently developed from the forward solutions. Furthermore, arbitrary excitation waveforms, such as a sinusoid or a square wave, for applications in conventional and transient eddy current, respectively, may be considered. Experimental results, obtained for a square wave excitation, are found to be in excellent agreement with the analytical predictions.